Type B equivariant foam categorification conjecture

Let $\mathbf{B}^n_m$ be the endomorphism category

$$\mathbf{B}^n_m:={\rm End}_{2n\mathbf{Foam_+}}(n^{\otimes m}),$$

and let $(\mathbf{B}^n_m)^\tau$ be the equivariant category associated with the involution $\tau$. The equivariant Grothendieck group $K_0^\tau((\mathbf{B}^n_m)^\tau)$ is obtained by imposing the relation $[-\mathbf{X}^{(k)}]=- [\mathbf{X}^{(k)}]$. Type B equivariant decategorification conjecture. There is an isomorphism

$${\mathbb C}(q)\otimes_{{\mathbb Z}[q^{\pm}]}K_0^\tau\big((\mathbf{B}^n_m)^\tau\big)\cong {\rm End}_{U_q(\mathfrak{so}_{2n+1})}(S^{\otimes m}).$$

This proposes that equivariant decategorification of the type $A$ foam category produces the type $B$ spin representation-theoretic web algebra, providing a categorified explanation of the folding paradigm. It is presented as a proposed general framework rather than an established result.